There's some truth to your second statement, but your first statement doesn't follow from it. If it was commonplace for people to get involved in altercations where they had to defend themselves with a weapon, it'd be both a better idea to start carrying a weapon if you weren't already, and it'd also discourage people from committing petty crimes like muggings. It might be worth it to a criminal to potentially lose their life over $1000, but not for $20.
You could make the argument that my statements logically extend to saying an armed populace increases larger more violent crimes while reducing the prevalence of petty crimes, and I agree that might make sense in a short-term, but criminals don't grow exponentially just because, crime is a symptom of separate social factors.
Fundamentally, there's no downside to carrying a weapon. If you don't need it, then you don't need it. If you do truly need to defend yourself with violence, then there isn't really much substitute and worse case you die wishing you'd had a weapon.